Bottom Line:
For this reason, coarse-grained models have been used successfully.The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes.The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Affiliation: Department of Computer Science, Iowa State University, Ames, Iowa, United States of America.

ABSTRACTDynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations--how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

pcbi.1004542.g002: Comparison of the coarse-graining time using the proposed method and the diagonalization time of the coarse-grained Hessian matrix.

Mentions:
Fig 2 shows the efficiency (computational time) of the proposed method as a function of the system size. In the figure, each blue and red point represent respectively, for a protein of that size, the coarse-graining time, i.e., the time required to construct the coarse-grained ssNMA Hessian matrix (with ξ = 0.01), and the diagonalization time of that coarse-grained Hessian matrix. The dashed lines show the growth rates of the time cost as a function of the system size. The curves are obtained from the least squares fitting to a non-linear function f(x) = axb. As shown in the figure, the diagonalization time (red curve) grows approximately as the cube, while the coarse-graining time grows approximately linearly. Especially for large complexes, the time needed for coarse-graining the all-atom Hessian matrix using Algorithm 1 becomes increasingly smaller relative to the diagonalization time. As a result, the total time for computing the normal modes for such large protein complexes using the coarse-grained ssNMA Hessian matrices is about the same as for other coarse-grained elastic network models such as ANM.

pcbi.1004542.g002: Comparison of the coarse-graining time using the proposed method and the diagonalization time of the coarse-grained Hessian matrix.

Mentions:
Fig 2 shows the efficiency (computational time) of the proposed method as a function of the system size. In the figure, each blue and red point represent respectively, for a protein of that size, the coarse-graining time, i.e., the time required to construct the coarse-grained ssNMA Hessian matrix (with ξ = 0.01), and the diagonalization time of that coarse-grained Hessian matrix. The dashed lines show the growth rates of the time cost as a function of the system size. The curves are obtained from the least squares fitting to a non-linear function f(x) = axb. As shown in the figure, the diagonalization time (red curve) grows approximately as the cube, while the coarse-graining time grows approximately linearly. Especially for large complexes, the time needed for coarse-graining the all-atom Hessian matrix using Algorithm 1 becomes increasingly smaller relative to the diagonalization time. As a result, the total time for computing the normal modes for such large protein complexes using the coarse-grained ssNMA Hessian matrices is about the same as for other coarse-grained elastic network models such as ANM.

Bottom Line:
For this reason, coarse-grained models have been used successfully.The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes.The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.

Affiliation:
Department of Computer Science, Iowa State University, Ames, Iowa, United States of America.

ABSTRACTDynamics can provide deep insights into the functional mechanisms of proteins and protein complexes. For large protein complexes such as GroEL/GroES with more than 8,000 residues, obtaining a fine-grained all-atom description of its normal mode motions can be computationally prohibitive and is often unnecessary. For this reason, coarse-grained models have been used successfully. However, most existing coarse-grained models use extremely simple potentials to represent the interactions within the coarse-grained structures and as a result, the dynamics obtained for the coarse-grained structures may not always be fully realistic. There is a gap between the quality of the dynamics of the coarse-grained structures given by all-atom models and that by coarse-grained models. In this work, we resolve an important question in protein dynamics computations--how can we efficiently construct coarse-grained models whose description of the dynamics of the coarse-grained structures remains as accurate as that given by all-atom models? Our method takes advantage of the sparseness of the Hessian matrix and achieves a high efficiency with a novel iterative matrix projection approach. The result is highly significant since it can provide descriptions of normal mode motions at an all-atom level of accuracy even for the largest biomolecular complexes. The application of our method to GroEL/GroES offers new insights into the mechanism of this biologically important chaperonin, such as that the conformational transitions of this protein complex in its functional cycle are even more strongly connected to the first few lowest frequency modes than with other coarse-grained models.